Related papers: An $hp$-adaptive multi-element stochastic collocat…
In this paper, we develop an adaptive finite element method for the nonlinear steady-state Poisson-Nernst-Planck equations, where the spatial adaptivity for geometrical singularities and boundary layer effects are mainly considered. As a…
In this paper, we introduce and analyze a new low-rank multilevel strategy for the solution of random diffusion problems. Using a standard stochastic collocation scheme, we first approximate the infinite dimensional random problem by a…
Over the last few years there have been dramatic advances in our understanding of mathematical and computational models of complex systems in the presence of uncertainty. This has led to a growth in the area of uncertainty quantification as…
The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric…
Background In proteomics, the most probable localizations of post-translational modifications are assessed by localization scores evaluating the likelihood of a given modification to occupy a site on a peptide sequence. When identifying…
In this paper we extend the hierarchical model reduction framework based on reduced basis techniques for the application to nonlinear partial differential equations. The major new ingredient to accomplish this goal is the introduction of…
This work explores a novel approach for adaptive, differentiable parametrization of large-scale non-stationary random fields. Coupled with any gradient-based algorithm, the method can be applied to variety of optimization problems,…
We consider a class of stochastic programming problems where the implicitly decision-dependent random variable follows a nonparametric regression model with heteroscedastic error. The Clarke subdifferential and surrogate functions are not…
We propose a stochastic multiscale finite element method (StoMsFEM) to solve random elliptic partial differential equations with a high stochastic dimension. The key idea is to simultaneously upscale the stochastic solutions in the physical…
In this paper, we present a new adaptive rank approximation technique for computing solutions to the high-dimensional linear kinetic transport equation. The approach we propose is based on a macro-micro decomposition of the kinetic model in…
We propose a new practical adaptive refinement strategy for $hp$-finite element approximations of elliptic problems. Following recent theoretical developments in polynomial-degree-robust a posteriori error analysis, we solve two types of…
This paper introduces an elasticity reconstruction method based on local displacement observations of elastic bodies. Sparse reconstruction theory is applied to formulate the underdetermined inverse problems of elasticity reconstruction…
A recently developed upscaling technique, the multicontinuum homogenization method, has gained significant attention for its effectiveness in modeling complex multiscale systems. This method defines multiple continua based on distinct…
Leja points on a compact $K \subset \mathbb{C}$ are known to provide efficient points for interpolation, but their actual implementation can be computationally challenging. So-called pseudo Leja points are a more tractable solution, yet…
The versatile physical properties of heterogeneous materials are intimately related to their complex microstructures, which can be statistically characterized and modelled using various spatial correlation functions containing key…
This thesis presents recent advances in model order reduction methods with the primary aim to construct online-efficient reduced surrogate models for parameterized multiscale phenomena and accelerate large-scale PDE-constrained parameter…
In this paper, we propose SubLoRA, a rank determination method for Low-Rank Adaptation (LoRA) based on submodular function maximization. In contrast to prior approaches, such as AdaLoRA, that rely on first-order (linearized) approximations…
In this paper, we present a family of new mixed finite element methods for linear elasticity for both spatial dimensions $n=2,3$, which yields a conforming and strongly symmetric approximation for stress. Applying…
Periodic dynamical systems ubiquitously exist in science and engineering. The harmonic balance (HB) method and its variants have been the most widely-used approaches for such systems, but are either confined to low-order approximations or…
Supervised deep-embedding methods project inputs of a domain to a representational space in which same-class instances lie near one another and different-class instances lie far apart. We propose a probabilistic method that treats…